Matthew S. Bauer ’10 and Dr. Xizhong Zheng, Associate Professor of Computer Science and Mathematics, co-authored a paper “On the Weak Computability of Continuous Real Functions” that was accepted for the Seventh International Conference of Computability and Complexity in Analysis held this week, June 21-25, in Zhenjiang, China.
Bauer presented the research at the conference in China on Tuesday, June 22. He studied with Zheng for three semesters, and received a scholarship to attend Villanova University’s master’s program in computer science in the fall. This summer, Bauer has an internship position at Gnostech in Warminster, Pa. “I worked on a number of different research projects during the course of my undergraduate studies. For one project, Dr. Yanxia Jia, Assistant Professor of Computer Science, and I were trying to develop a home-monitoring system using a network of sensors. The sensors we used are developmental sensors developed by SUN micro-systems called SPOTS. We developed a user interface that graphs temperate readings of the spots and also shows the connectivity of the network. Dr. Jia also helped me get into a Research Experience for Undergraduates at the University of Texas at San Antonio last summer. This program lasted for one summer, and our focus was on developing a system of unmanned ground and air vehicles (robots) with the ability to effectively navigate a terrain.
“The biggest research project I was involved in, was working with Dr. Zheng on the computability of real functions. We introduced a new class of functions that can be computed with less effective error bounds. The project began last year and Dr. Zheng and I would meet once a week to discuss material from a book he gave me to read. At this point, our working together was not associated with any class, and I am very grateful that Dr. Zheng was willing to work with me on a purely volunteer basis. After this, we continued our research in a one-year Capstone project. Dr. Zheng was very patient in working with me and explaining new concepts.
“Working with faculty has been my most valuable experience here at Arcadia,” Bauer adds. “It has allowed me to develop closer bonds with my professors and to extend my knowledge far beyond what I learned in the classroom. My project with Dr. Zheng has also lead to a joint publication that I now have the opportunity to present at the 10th annual Computability and Complexity in Analysis conference in China. This publication will also gave me a tremendous advantage when applying to graduate schools.”
A double major in Mathematics and Computer Science, Bauer graduated summa cum laude with departmental honors in May. He received the Sigma Zeta Award in Computer Science for academic excellence in computer science at Honors Convocation, as well as receiving an Ellington Beavers Award for Intellectual Inquiry and being inducted into Phi Kappa Phi as a junior. He completed 450 hours of community service with the AmeriCorps Community Service program, and was a Peer Assisted Study Session (PASS) Tutor and Math Lab tutor. He also helped raise money for the Save a Child Foundation to build a library for children in Akatsi, Ghana. He was active in Arcadia’s International Club and the Asian Students in America (ASIA) club. Bauer graduated from Downingtown (Pa.) West High School.
According to the abstract of the paper by Bauer and Zheng, “In computable analysis, sequences of rational numbers which effectively converge to a real number x are used as the (rho-) names of x,” writes Bauer in the abstract. “A real number x is computable if it has a computable name, and a real function f is computable if there is a Turing machine M which computes f in the sense that, M accepts any rho-name of x as input and outputs a rho-name of f(x) for any x in the domain of f. By weakening the effectiveness requirement of the convergence and classifying the converging speeds of rational sequences, several interesting classes of real numbers of weak computability have been introduced in literature, e.g., in addition to the class of computable real numbers (EC), we have the classes of semi-computable (SC), weakly computable (WC), divergence bounded computable (DBC) and computably approximable real numbers (CA).
“In this paper, we are interested in the weak computability of continuous real functions and try to introduce an analogous classification of weakly computable real functions. We present definitions of these functions by Turing machines as well as by sequences of rational polygons and prove these two definitions are not equivalent. Furthermore, we explore the properties of these functions, and among others, show their closure properties under arithmetic operations and composition.”